In this paper, we present metriplectic extensions of the Lie–Poisson dynamics of fluid flows over the unit annulus for both the Lebesgue [Formula: see text]-pairing and the Sobolev [Formula: see text]-pairing. Several examples are provided including 2D Nav ...
The restricted Siegel disc is a homogeneous space related to the con- nected component To(1) of the universal Teichmller space via the period mapping. In this paper, we show that it is a coadjoint orbit of the universal central extension of the restricted ...
The aim of this paper is to develop, for the first time, a general theory of simultaneous local normalisation of couples (X,G), where X is a dynamical system (vector field) and G is an underlying geometric structure preserved by X, even if both have singul ...
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained variational principles fo ...
Frobenius reciprocity asserts that induction from a subgroup and restriction to it are adjoint functors in categories of unitary G-modules. In the 1980s, Guillemin and Sternberg established a parallel property of Hamiltonian G-spaces, which (as we show) un ...
We introduce the three-dimensional Eringen system of equations for the nematodynamics of liquid crystals, announce the short time existence and uniqueness of strong solutions for the one-dimensional problem in the periodic case, and show the continuous dep ...
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We introduce Wigner measures for infinite-dimensional open quantum systems; important examples of such systems are encountered in quantum control theory. In addition, we propose an axiomatic definition of coherent quantum feedback. ...
The geodesic flows are studied on real forms of complex semi-simple Lie groups with respect to a left-invariant (pseudo-)Riemannian metric of rigid body type. The Williamson types of the isolated relative equilibria on generic adjoint orbits are determined ...
We address the problem concerning the origin of quantum anomalies, which has been the source of disagreement in the literature. Our approach is novel as it is based on the differentiability properties of families of generalized measures. To this end, we in ...
In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...
Certain kinematic optimal control problems (the Clebsch problems) and their connection to classical integrable systems are considered. In particular, the rigid body problem and its rank 2k counterparts, the geodesic flows on Stiefel manifolds and their con ...
In this paper, we study the three-dimensional Ericksen-Leslie equations for the nematodynamics of liquid crystals. We prove short time existence and uniqueness of strong solutions for the initial value problem for the periodic case and in bounded domains w ...
We present a structure preserving numerical algorithm for the collision of elastic bodies. Our integrator is derived from a discrete version of the field-theoretic (multisymplectic) variational description of nonsmooth Lagrangian continuum mechanics, combi ...
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...
A quantum anomaly is the breaking of symmetry with respect to some transformations after the quantization of a classical Hamiltonian or Lagrangian system. It is shown that both the Noether theorems (including their infinite-dimensional versions) and the ex ...
We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semi ...
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 -245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quas ...
In this paper we study the two dimensional Ericksen-Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value ...
